Previous form of the Hamiltonian density on the reduced phase space is valid for \(a\ne 0\) . Explicitly, it is not valid for \(\alpha =-\frac{1}{2}\) , that, according to
[1]}, [2]}, [3]}, defines temporal gauge
\(\phi =x^++x^- \ , \quad t=x^+ \ , \quad p_t=p_+-p_- \ , \quad p_\phi =p_- \ .\) 
